Korean J. Math. Vol. 21 No. 3 (2013) pp.331-344
DOI: https://doi.org/10.11568/kjm.2013.21.3.331

Higher cyclotomic units for motivic cohomology

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Sung Myung


In the present article, we describe specific elements in a motivic cohomology group $H^1_{M} \bigl( Spec Q (\zeta_l), \, Z(2) \bigr)$ of cyclotomic fields,
which generate a subgroup of finite index for an odd prime $l$. As $H^1_{M} \bigl( Spec Q (\zeta_l), \, Z(1) \bigr)$ is identified with the group of units in the ring of integers
in $Q (\zeta_l)$ and cyclotomic units generate a subgroup of finite index, these elements play similar roles in the motivic cohomology group.

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